Polytope of Type {28,16,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,16,2}*1792b
if this polytope has a name.
Group : SmallGroup(1792,323453)
Rank : 4
Schlafli Type : {28,16,2}
Number of vertices, edges, etc : 28, 224, 16, 2
Order of s₀s₁s₂s₃ : 112
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {28,8,2}*896a
   4-fold quotients : {28,4,2}*448, {14,8,2}*448
   7-fold quotients : {4,16,2}*256b
   8-fold quotients : {28,2,2}*224, {14,4,2}*224
   14-fold quotients : {4,8,2}*128a
   16-fold quotients : {14,2,2}*112
   28-fold quotients : {4,4,2}*64, {2,8,2}*64
   32-fold quotients : {7,2,2}*56
   56-fold quotients : {2,4,2}*32, {4,2,2}*32
   112-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.

Permutation Representation (GAP) :

s0 := (  1,113)(  2,119)(  3,118)(  4,117)(  5,116)(  6,115)(  7,114)(  8,120)(  9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,127)( 16,133)( 17,132)( 18,131)( 19,130)( 20,129)( 21,128)( 22,134)( 23,140)( 24,139)( 25,138)( 26,137)( 27,136)( 28,135)( 29,141)( 30,147)( 31,146)( 32,145)( 33,144)( 34,143)( 35,142)( 36,148)( 37,154)( 38,153)( 39,152)( 40,151)( 41,150)( 42,149)( 43,155)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)( 49,156)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)( 57,176)( 58,182)( 59,181)( 60,180)( 61,179)( 62,178)( 63,177)( 64,169)( 65,175)( 66,174)( 67,173)( 68,172)( 69,171)( 70,170)( 71,190)( 72,196)( 73,195)( 74,194)( 75,193)( 76,192)( 77,191)( 78,183)( 79,189)( 80,188)( 81,187)( 82,186)( 83,185)( 84,184)( 85,204)( 86,210)( 87,209)( 88,208)( 89,207)( 90,206)( 91,205)( 92,197)( 93,203)( 94,202)( 95,201)( 96,200)( 97,199)( 98,198)( 99,218)(100,224)(101,223)(102,222)(103,221)(104,220)(105,219)(106,211)(107,217)(108,216)(109,215)(110,214)(111,213)(112,212)(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,344)(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,351)(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,358)(247,364)(248,363)(249,362)(250,361)(251,360)(252,359)(253,365)(254,371)(255,370)(256,369)(257,368)(258,367)(259,366)(260,372)(261,378)(262,377)(263,376)(264,375)(265,374)(266,373)(267,379)(268,385)(269,384)(270,383)(271,382)(272,381)(273,380)(274,386)(275,392)(276,391)(277,390)(278,389)(279,388)(280,387)(281,400)(282,406)(283,405)(284,404)(285,403)(286,402)(287,401)(288,393)(289,399)(290,398)(291,397)(292,396)(293,395)(294,394)(295,414)(296,420)(297,419)(298,418)(299,417)(300,416)(301,415)(302,407)(303,413)(304,412)(305,411)(306,410)(307,409)(308,408)(309,428)(310,434)(311,433)(312,432)(313,431)(314,430)(315,429)(316,421)(317,427)(318,426)(319,425)(320,424)(321,423)(322,422)(323,442)(324,448)(325,447)(326,446)(327,445)(328,444)(329,443)(330,435)(331,441)(332,440)(333,439)(334,438)(335,437)(336,436);;
s1 := (  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 23)( 16, 22)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 29, 30)( 31, 35)( 32, 34)( 36, 37)( 38, 42)( 39, 41)( 43, 51)( 44, 50)( 45, 56)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 57, 72)( 58, 71)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 73)( 64, 79)( 65, 78)( 66, 84)( 67, 83)( 68, 82)( 69, 81)( 70, 80)( 85,100)( 86, 99)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,107)( 93,106)( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)(113,142)(114,141)(115,147)(116,146)(117,145)(118,144)(119,143)(120,149)(121,148)(122,154)(123,153)(124,152)(125,151)(126,150)(127,163)(128,162)(129,168)(130,167)(131,166)(132,165)(133,164)(134,156)(135,155)(136,161)(137,160)(138,159)(139,158)(140,157)(169,212)(170,211)(171,217)(172,216)(173,215)(174,214)(175,213)(176,219)(177,218)(178,224)(179,223)(180,222)(181,221)(182,220)(183,198)(184,197)(185,203)(186,202)(187,201)(188,200)(189,199)(190,205)(191,204)(192,210)(193,209)(194,208)(195,207)(196,206)(225,282)(226,281)(227,287)(228,286)(229,285)(230,284)(231,283)(232,289)(233,288)(234,294)(235,293)(236,292)(237,291)(238,290)(239,303)(240,302)(241,308)(242,307)(243,306)(244,305)(245,304)(246,296)(247,295)(248,301)(249,300)(250,299)(251,298)(252,297)(253,310)(254,309)(255,315)(256,314)(257,313)(258,312)(259,311)(260,317)(261,316)(262,322)(263,321)(264,320)(265,319)(266,318)(267,331)(268,330)(269,336)(270,335)(271,334)(272,333)(273,332)(274,324)(275,323)(276,329)(277,328)(278,327)(279,326)(280,325)(337,429)(338,428)(339,434)(340,433)(341,432)(342,431)(343,430)(344,422)(345,421)(346,427)(347,426)(348,425)(349,424)(350,423)(351,436)(352,435)(353,441)(354,440)(355,439)(356,438)(357,437)(358,443)(359,442)(360,448)(361,447)(362,446)(363,445)(364,444)(365,401)(366,400)(367,406)(368,405)(369,404)(370,403)(371,402)(372,394)(373,393)(374,399)(375,398)(376,397)(377,396)(378,395)(379,408)(380,407)(381,413)(382,412)(383,411)(384,410)(385,409)(386,415)(387,414)(388,420)(389,419)(390,418)(391,417)(392,416);;
s2 := (  1,225)(  2,226)(  3,227)(  4,228)(  5,229)(  6,230)(  7,231)(  8,232)(  9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,246)( 16,247)( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,239)( 23,240)( 24,241)( 25,242)( 26,243)( 27,244)( 28,245)( 29,260)( 30,261)( 31,262)( 32,263)( 33,264)( 34,265)( 35,266)( 36,253)( 37,254)( 38,255)( 39,256)( 40,257)( 41,258)( 42,259)( 43,267)( 44,268)( 45,269)( 46,270)( 47,271)( 48,272)( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)( 57,295)( 58,296)( 59,297)( 60,298)( 61,299)( 62,300)( 63,301)( 64,302)( 65,303)( 66,304)( 67,305)( 68,306)( 69,307)( 70,308)( 71,281)( 72,282)( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,289)( 80,290)( 81,291)( 82,292)( 83,293)( 84,294)( 85,330)( 86,331)( 87,332)( 88,333)( 89,334)( 90,335)( 91,336)( 92,323)( 93,324)( 94,325)( 95,326)( 96,327)( 97,328)( 98,329)( 99,316)(100,317)(101,318)(102,319)(103,320)(104,321)(105,322)(106,309)(107,310)(108,311)(109,312)(110,313)(111,314)(112,315)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,358)(128,359)(129,360)(130,361)(131,362)(132,363)(133,364)(134,351)(135,352)(136,353)(137,354)(138,355)(139,356)(140,357)(141,372)(142,373)(143,374)(144,375)(145,376)(146,377)(147,378)(148,365)(149,366)(150,367)(151,368)(152,369)(153,370)(154,371)(155,379)(156,380)(157,381)(158,382)(159,383)(160,384)(161,385)(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)(169,407)(170,408)(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)(177,415)(178,416)(179,417)(180,418)(181,419)(182,420)(183,393)(184,394)(185,395)(186,396)(187,397)(188,398)(189,399)(190,400)(191,401)(192,402)(193,403)(194,404)(195,405)(196,406)(197,442)(198,443)(199,444)(200,445)(201,446)(202,447)(203,448)(204,435)(205,436)(206,437)(207,438)(208,439)(209,440)(210,441)(211,428)(212,429)(213,430)(214,431)(215,432)(216,433)(217,434)(218,421)(219,422)(220,423)(221,424)(222,425)(223,426)(224,427);;
s3 := (449,450);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(450)!(  1,113)(  2,119)(  3,118)(  4,117)(  5,116)(  6,115)(  7,114)(  8,120)(  9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,127)( 16,133)( 17,132)( 18,131)( 19,130)( 20,129)( 21,128)( 22,134)( 23,140)( 24,139)( 25,138)( 26,137)( 27,136)( 28,135)( 29,141)( 30,147)( 31,146)( 32,145)( 33,144)( 34,143)( 35,142)( 36,148)( 37,154)( 38,153)( 39,152)( 40,151)( 41,150)( 42,149)( 43,155)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)( 49,156)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)( 57,176)( 58,182)( 59,181)( 60,180)( 61,179)( 62,178)( 63,177)( 64,169)( 65,175)( 66,174)( 67,173)( 68,172)( 69,171)( 70,170)( 71,190)( 72,196)( 73,195)( 74,194)( 75,193)( 76,192)( 77,191)( 78,183)( 79,189)( 80,188)( 81,187)( 82,186)( 83,185)( 84,184)( 85,204)( 86,210)( 87,209)( 88,208)( 89,207)( 90,206)( 91,205)( 92,197)( 93,203)( 94,202)( 95,201)( 96,200)( 97,199)( 98,198)( 99,218)(100,224)(101,223)(102,222)(103,221)(104,220)(105,219)(106,211)(107,217)(108,216)(109,215)(110,214)(111,213)(112,212)(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,344)(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,351)(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,358)(247,364)(248,363)(249,362)(250,361)(251,360)(252,359)(253,365)(254,371)(255,370)(256,369)(257,368)(258,367)(259,366)(260,372)(261,378)(262,377)(263,376)(264,375)(265,374)(266,373)(267,379)(268,385)(269,384)(270,383)(271,382)(272,381)(273,380)(274,386)(275,392)(276,391)(277,390)(278,389)(279,388)(280,387)(281,400)(282,406)(283,405)(284,404)(285,403)(286,402)(287,401)(288,393)(289,399)(290,398)(291,397)(292,396)(293,395)(294,394)(295,414)(296,420)(297,419)(298,418)(299,417)(300,416)(301,415)(302,407)(303,413)(304,412)(305,411)(306,410)(307,409)(308,408)(309,428)(310,434)(311,433)(312,432)(313,431)(314,430)(315,429)(316,421)(317,427)(318,426)(319,425)(320,424)(321,423)(322,422)(323,442)(324,448)(325,447)(326,446)(327,445)(328,444)(329,443)(330,435)(331,441)(332,440)(333,439)(334,438)(335,437)(336,436);
s1 := Sym(450)!(  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 23)( 16, 22)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 29, 30)( 31, 35)( 32, 34)( 36, 37)( 38, 42)( 39, 41)( 43, 51)( 44, 50)( 45, 56)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 57, 72)( 58, 71)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 73)( 64, 79)( 65, 78)( 66, 84)( 67, 83)( 68, 82)( 69, 81)( 70, 80)( 85,100)( 86, 99)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,107)( 93,106)( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)(113,142)(114,141)(115,147)(116,146)(117,145)(118,144)(119,143)(120,149)(121,148)(122,154)(123,153)(124,152)(125,151)(126,150)(127,163)(128,162)(129,168)(130,167)(131,166)(132,165)(133,164)(134,156)(135,155)(136,161)(137,160)(138,159)(139,158)(140,157)(169,212)(170,211)(171,217)(172,216)(173,215)(174,214)(175,213)(176,219)(177,218)(178,224)(179,223)(180,222)(181,221)(182,220)(183,198)(184,197)(185,203)(186,202)(187,201)(188,200)(189,199)(190,205)(191,204)(192,210)(193,209)(194,208)(195,207)(196,206)(225,282)(226,281)(227,287)(228,286)(229,285)(230,284)(231,283)(232,289)(233,288)(234,294)(235,293)(236,292)(237,291)(238,290)(239,303)(240,302)(241,308)(242,307)(243,306)(244,305)(245,304)(246,296)(247,295)(248,301)(249,300)(250,299)(251,298)(252,297)(253,310)(254,309)(255,315)(256,314)(257,313)(258,312)(259,311)(260,317)(261,316)(262,322)(263,321)(264,320)(265,319)(266,318)(267,331)(268,330)(269,336)(270,335)(271,334)(272,333)(273,332)(274,324)(275,323)(276,329)(277,328)(278,327)(279,326)(280,325)(337,429)(338,428)(339,434)(340,433)(341,432)(342,431)(343,430)(344,422)(345,421)(346,427)(347,426)(348,425)(349,424)(350,423)(351,436)(352,435)(353,441)(354,440)(355,439)(356,438)(357,437)(358,443)(359,442)(360,448)(361,447)(362,446)(363,445)(364,444)(365,401)(366,400)(367,406)(368,405)(369,404)(370,403)(371,402)(372,394)(373,393)(374,399)(375,398)(376,397)(377,396)(378,395)(379,408)(380,407)(381,413)(382,412)(383,411)(384,410)(385,409)(386,415)(387,414)(388,420)(389,419)(390,418)(391,417)(392,416);
s2 := Sym(450)!(  1,225)(  2,226)(  3,227)(  4,228)(  5,229)(  6,230)(  7,231)(  8,232)(  9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,246)( 16,247)( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,239)( 23,240)( 24,241)( 25,242)( 26,243)( 27,244)( 28,245)( 29,260)( 30,261)( 31,262)( 32,263)( 33,264)( 34,265)( 35,266)( 36,253)( 37,254)( 38,255)( 39,256)( 40,257)( 41,258)( 42,259)( 43,267)( 44,268)( 45,269)( 46,270)( 47,271)( 48,272)( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)( 57,295)( 58,296)( 59,297)( 60,298)( 61,299)( 62,300)( 63,301)( 64,302)( 65,303)( 66,304)( 67,305)( 68,306)( 69,307)( 70,308)( 71,281)( 72,282)( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,289)( 80,290)( 81,291)( 82,292)( 83,293)( 84,294)( 85,330)( 86,331)( 87,332)( 88,333)( 89,334)( 90,335)( 91,336)( 92,323)( 93,324)( 94,325)( 95,326)( 96,327)( 97,328)( 98,329)( 99,316)(100,317)(101,318)(102,319)(103,320)(104,321)(105,322)(106,309)(107,310)(108,311)(109,312)(110,313)(111,314)(112,315)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,358)(128,359)(129,360)(130,361)(131,362)(132,363)(133,364)(134,351)(135,352)(136,353)(137,354)(138,355)(139,356)(140,357)(141,372)(142,373)(143,374)(144,375)(145,376)(146,377)(147,378)(148,365)(149,366)(150,367)(151,368)(152,369)(153,370)(154,371)(155,379)(156,380)(157,381)(158,382)(159,383)(160,384)(161,385)(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)(169,407)(170,408)(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)(177,415)(178,416)(179,417)(180,418)(181,419)(182,420)(183,393)(184,394)(185,395)(186,396)(187,397)(188,398)(189,399)(190,400)(191,401)(192,402)(193,403)(194,404)(195,405)(196,406)(197,442)(198,443)(199,444)(200,445)(201,446)(202,447)(203,448)(204,435)(205,436)(206,437)(207,438)(208,439)(209,440)(210,441)(211,428)(212,429)(213,430)(214,431)(215,432)(216,433)(217,434)(218,421)(219,422)(220,423)(221,424)(222,425)(223,426)(224,427);
s3 := Sym(450)!(449,450);
poly := sub<Sym(450)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope